Analytic Derivatives for Estimation of Discrete-Time, Linear-Quadratic, Dynamic, Optimization Models

Econometrica ◽  
1988 ◽  
Vol 56 (2) ◽  
pp. 467 ◽  
Author(s):  
Peter Zadrozny
Keyword(s):  
Dynamic Optimization ◽  
Discrete Time ◽  
Optimization Models ◽  
Linear Quadratic ◽  
Time Linear

Calculation of Optimized Movement Trajectories for the Human Forearm

2013 ◽  
Vol 401-403 ◽  
pp. 1347-1352
Author(s):  
Li Li Yang
Keyword(s):  
Discrete Time ◽  
Linear Quadratic Regulator ◽  
Minimum Variance ◽  
Movement Trajectory ◽  
Linear Quadratic ◽  
Variance Model ◽  
Movement Trajectories ◽  
Human Forearm ◽  
Optimal Movement ◽  
Time Linear

Using the minimum variance model, optimal human forearm trajectories formation was investigated using a discrete time linear quadratic regulator. First, the continuous dynamics of the human forearm were established on the basis of the relation between muscle torque and neural control signal, and then we transferred the continuous system dynamics to discrete time notation. Finally we expressed the objective function of minimum variance model using a discrete time linear quadratic regulator and employed Riccati recursion to obtain the optimal movement trajectories of the human forearm. The results of example simulation show that the optimal movement trajectory of the forearm follows a smooth curve, and the speed curve of the hand is single peaked and bell shaped. These are in good agreement with the inherent kinematic properties of optimal movement, and therefore the method is effective for calculating the optimal movement trajectory of the human forearm.

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